This application claims Paris Convention priority of DE 198 48 687.1 filed Oct. 22, 1998 the complete disclosure of which is hereby incorporated by reference.
Conventional continuous or discontinuous measuring capillary viscometers or rheometers determine the pressure difference between the input and the output of a measuring capillary having constant cross section through which a measuring liquid flows. The volume flow and the pressure differences can be used in conjunction with the dimensions of the capillary to determine a characteristic flow quantity (the xe2x80x9cviscosityxe2x80x9d) for the liquid. The constant cross section of the capillary leads to pure shear flow and this xe2x80x9cviscosityxe2x80x9d is the shear viscosity xcex7,
xcex7=xcfx84/{dot over (xcex3)}xe2x80x83xe2x80x83(1)
where xcfx84 is the shear stress and {dot over (xcex3)} the shear velocity. For Newtonian liquids whose shear viscosity is independent of the shear velocity, xcex7 can be directly calculated from these measurements using conventional equations (Hagen-Poiseuille law).
A plurality of technical liquids (materials which occur in the liquid state during manufacturing processes) are non-Newtonian liquids whose viscosity depends on the shear velocity (for a given capillary dimension of volume flow). Principal examples therefor are primarily polymer melts and polymer solutions. In order to describe their flow behavior, viscosity functions or other flow functions, e.g. the shear-stress function, are required. The shear-stress function describes the shear stress in dependence on the shear velocity xcfx84=f(xcex3). In a capillary rheometer of constant capillary cross section, only xe2x80x9capparentxe2x80x9d viscosity values can be determined for these liquids, at constant volume flow, i.e. the Newtonian flow equation is utilized for the calculation.
In order to determined a flow function or parts of a flow function for process monitoring purposes, capillary rheometers have been used in recent times having wedge shaped or conical capillaries (see for example laid open publication DE-A-42 36 407, U.S. Pat. No. 4624 132 and A. Papendinskas, W. R. Cluett, S. T. Balke in Polymer Engineering and Science Mid-March 1991, Vol. 31. No. 5, pages 365-375). Capillary rheometers of this kind are equipped with pressure measuring probes to measure the pressure drop across parts of the capillary. Using e.g. a wedge-shaped capillary equipped with at least three pressure measuring locations, the actual non-Newtonian viscosity, for the shear velocity within the capillary, can be determined for constant operating conditions (e.g. {dot over (V)}=a constant or xcex94p=a constant). If, within the range of shear velocities occurring between the input and output of such a capillary, the flow function can be described using a simple flow law such as that given by Ostwald and de Waele (also referred to as the potential law) in accordance with equation (2) or (3) below, then the flow law is also known for these capillaries.
xcfx84({dot over (xcex3)})=K{dot over (xcex3)}nxe2x80x83xe2x80x83(2)
xe2x80x83xcex7({dot over (xcex3)})=K{dot over (xcex3)}nxe2x88x921=K{dot over (xcex3)}mxe2x80x83xe2x80x83(3)
Such rheometers are utilized for on-line processing and quality control and, when operated at constant pressure differentials, can even directly provide quantitative information concerning the average molecular weight and the molecular weight distribution (DE-A-42 36 407).
Capillary rheometers having such narrowing or widening capillaries do not however produce pure shear flow so that the result does not lead to a pure shear viscosity in all cases. In such capillaries, the shear flow is overlapped with an additional extensional flow (extension of an extrusion liquid in consequence of the cross section narrowing) and the overall flow resistance is a combination of shear and extensional components. Analogous to the shear resistance which results from the shear viscosity xcex7 and the shear velocity {dot over (xcex3)}, the extensional resistance is caused by the extensional viscosity xcex7E and the extensional velocity {overscore (xcex5)}. The extensional resistance results from the tensile stress "sgr" produced in the flow. The extensional viscosity
xcex7E="sgr"/{dot over (xcex5)}xe2x80x83xe2x80x83(4)
is also designated Trouton-viscosity xcex7T and, for Newtonian liquids, is three times larger than the shear viscosity.
xcex7T=3xcex7xe2x80x83xe2x80x83(5)
In non-Newtonian liquids, in particular in plastic melts, this simple relationship as formulated in equation (5) is not satisfied. On the contrary, the ratio between xcex7E and xcex7 is often substantially more than three. In some fluids, xcex7E is even an order of magnitude larger than xcex7. The extent to which xcex7E exceeds xcex7 depends on the molecular properties and/or the molecular weight distribution of the plastic melt. In general, xcex7E does not depend on xcex7 and is only coupled to xcex7 via molecular or structural properties. The extensional viscosity of high molecular liquids is particular sensitive to very small fractions of large molecules and on the degree of branching of the macro-molecules (K. K. Chao et al. AIChE J. 30 (1984), page 111 ff; J. Ferguson, M.K.H El-Tawashi Proc. VIII Int. Congr. on Rheol. Vol. II, page 235 ff). However, the degree of branching changes the viscosity function only to a limited extent and can therefore not be determined using the shear viscosity. If shear viscosity or shear viscosity functions can be measured in a particular process, information is thereby available concerning the average value and width of the molecular weight distribution of the liquid. If, in addition and independently thereof, the extensional viscosity can be determined, changes in the range of very large molecules and changes in the degree of branching can be detected with high sensitivity. An independent material quantity is therefore available which is definitive for specific liquid and product properties to better describe the quality of a product in a comprehensive and directed fashion.
It is the underlying purpose of the invention to create a method and a device with which the shear viscosity (e.g. in the range of 10 mPasxe2x89xa6xcex7xe2x89xa6105 Pas) and the extensional viscosity (e.g. in the range 30 mPasxe2x89xa6xcex7Exe2x89xa6108 Pas) can be simultaneously determined on the same sample.
A method and apparatus with which the problem in accordance with the invention is solved is characterized in the patent claims.
Using a capillary having changing cross section and with a plurality of pressure measuring locations, the viscosity function of a liquid can be determined within a well defined shear velocity range under constant operating conditions (constant volume flow or pressure drop) (Papendinskas et al., DE-A-42 36 407). Although such capillaries do not have pure shear flow, the capillaries can be configured in such a fashion, e.g. having large length, that the influence of the extensional properties on the pressure drop is smaller than that of the shear properties by many orders of magnitude so that it can, in practice, be neglected. For a capillary of this type, the flow function is defined for the shear velocity range occurring between the input and the output.
The average extensional velocity {overscore ({dot over (xcex5)})} can be extracted from the difference between the average input and output velocities {overscore (V)}Axe2x88x92{overscore (V)}E, divided by the capillary length xcex94L (Equation (6)):                               ϵ                      .            _                          =                                                                              v                  _                                A                            -                                                v                  _                                E                                                    Δ              ⁢                              xe2x80x83                            ⁢              L                                =                                                                      V                  .                                /                                  F                  A                                            -                                                V                  .                                /                                  F                  E                                                                    Δ              ⁢                              xe2x80x83                            ⁢              L                                                          (        6        )            
The shear velocity {dot over (xcex3)}E and {dot over (xcex3)}A at the input and output are directly proportional to their average velocities {overscore (V)}E and {overscore (V)}A at the locations E and A, for constant cross section. A simple shortening of a wedge-shaped or conical capillary with otherwise constant input (FE) and output (FA) cross sections results, in accordance with equation (6), in a proportional increase in the average extensional velocity with constant shear velocity range between {dot over (xcex3)}E and {dot over (xcex3)}A. It has however been determined in accordance with the invention, that different relationships for shear and extensional flow losses are established in capillaries having wedged shapes or conical shapes of differing length with however equal cross sections so that shear viscosities and extensional viscosities can be separated under certain conditions using flows having similar geometries.
In accordance with Papendinskas et al., the pressure drop due to shear viscosity for Newtonian or for potential liquids, across a wedge-shaped capillary for otherwise constant cross sections (i.e. equal shear velocities from {dot over (xcex3)}E to {dot over (xcex3)}A), is directly proportional to the length of the capillary. Long capillaries therefore result in a larger viscous pressure drop. As can be seen from equation (6), long capillaries lead to a small extensional velocity {overscore ({dot over (xcex5)})} and, in accordance with equation (4), the tensile stress "sgr" is small. Long wedge-shaped or conical capillaries produce substantially viscous resistance and facilitate the direct determination of the viscosity or the viscosity function between the shear velocities {dot over (xcex3)}E and {dot over (xcex3)}A.
A very short wedge-shaped or conical capillary having the same inlet and outlet cross sections as a long capillary produces, for constant volume flow, a lower pressure difference due to shear viscosity. However, the extensional velocity increases in accordance with equation (6) and the additional pressure difference resulting from this extensional viscosity increases strongly in comparison to the pressure loss due to shearing. The invention uses this realization in order to develop a method and a device with which the shear viscosity and the extensional viscosity can be separated in one single method step. The shear viscosity and the extensional viscosity can thereby be simultaneously determined in the same sample.
The invention has a plurality of advantages. The shear viscosity is measured over an entire shear velocity range and the extensional viscosity is determined for a well-defined average extensional velocity on the same sample and in one method step. Assumptions concerning unknown flow and/or pressure processes are thereby unnecessary. The method and the apparatus are robust and can be utilized discontinuously in a laboratory or in a continuously operating apparatus, directly during a manufacturing or processing procedure without loosing time for data determination to effect quality control or even for processing control.
The method can be realized in a simple apparatus consisting of well defined capillaries connected in series, one behind the other. The invention is described more closely with regard to embodiments and the drawings.